We provide a new geometric description of the mKdV ows by showing that the (focusing) mKdV hierarchy can be realized by local motionsof Legendrian curves in he pseudohermitian Heisenberg group H^3. Indeed, a local motion of a Legendrian curve induces a local evolution equation for its pseudohermitian curvature. A sequence of motions is constructed whose curvature equations coincide with the evolution equations of the mKdV hierarchy.
INTEGRABLE FLOWS FOR LEGENDRIAN CURVES IN THE HEISENBERG GROUP / Musso, E., Nicolodi, L.. - (2026), pp. 1-15.
INTEGRABLE FLOWS FOR LEGENDRIAN CURVES IN THE HEISENBERG GROUP
Emilio Musso;Lorenzo Nicolodi
2026-01-01
Abstract
We provide a new geometric description of the mKdV ows by showing that the (focusing) mKdV hierarchy can be realized by local motionsof Legendrian curves in he pseudohermitian Heisenberg group H^3. Indeed, a local motion of a Legendrian curve induces a local evolution equation for its pseudohermitian curvature. A sequence of motions is constructed whose curvature equations coincide with the evolution equations of the mKdV hierarchy.File in questo prodotto:
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